Question

In about 5 billion years, at the end of its lifetime, our sun will end up as a white dwarf, having about the same mass as it does now, but reduced to about 15,000 km in diameter. What will be its density at that stage? In g/cm^3

Answer 1

The formula of density is given by

Density = Mass ÷ Volume

We have:
Mass = 1.989 × 10³⁰ kg
Volume = $\frac{4}{3} \pi r^3$ = $\frac{4}{3} \pi (7500)^3 = 1.767*10^12$ km³

Density = $\frac{(1.989)(10^{30})}{(1.767)(10^{12})}$=1.13×10¹⁸ kg/km³

Converting 1.13 × 10¹⁸ kg/km³ to g/cm³

1.13 × 10¹⁸ kg = 1.13 × 10¹⁸ × 10³ = 1.13 × 10²¹ grams
1 km³ = 1 × 10⁶ cm³ 

(1.13 × 10²¹) ÷ 10⁶ = 1.13 × 10¹⁵ gr/cm³

Answer: Density 1.13 × 10¹⁵ gr/cm³

Answer 2

1.125 x 10⁶ g/cm³.

Further explanation

Given:

• The mass of the sun = 1.989 x 10³⁰ kg
• The final diameter of the sun = 15,000 km

Question:  

What will represent the density of our sun at the end of its lifetime? (in g/cm³)

The Process:  

In the beginning, we calculate the volume of our sun which will end up like a white dwarf.

Let's assume the sun as a perfect sphere.  

Prepare the radius, i.e., $\boxed{ \ R = \frac{1}{2} \times diameter \ }$

$\boxed{ \ R = \frac{1}{2} \times 15,000 \ km \ } \rightarrow \boxed{ \ 7,500 \ km \ }$

Volume of sphere $\boxed{ \ V = \frac{4}{3} \pi R^3 \ }$

$\boxed{ \ V = \frac{4}{3} \pi (7,500)^3 \ }$

We deliver the volume of the sun at the stage, i.e., $\boxed{ \ V = 1.767 \times 10^{12} \ km^3 \ }$

Let us convert km³ to cm³ by multiplying $\boxed{ \ (10^3)^5 \rightarrow 10^{15} \ }$

$\boxed{ \ V = 1.767 \times 10^{12} \times 10^{15} \ cm^3 \ } \rightarrow \boxed{ \ V = 1.767 \times 10^{27} \ cm^3} \ }$ \ }[/tex]

After preparing the volume, then we proceed with calculating its density. The formula of density is provided by $\boxed{ \ Density = \frac{mass}{volume} \ }$

$\boxed{ \ Density = \frac{1.989 x 10^{30} \ kg}{1.767 \times 10^{27} \ cm^3} \ }$

Let us convert kg to gram by multiplying 10³.

$\boxed{ \ Density = \frac{1.989 x 10^{33} \ g}{1.767 \times 10^{27} \ cm^3} \ }$

Thus, the density of our sun at the end of its lifetime approximately will be $\boxed{\boxed{ \ 1.125 \times 10^6 \ g/cm^3 \ }}$  

Learn more

1. About the mass and density of substances  brainly.com/question/4053884
2. The energy density of the stored energy  brainly.com/question/9617400
3. The theoretical density of platinum which has the FCC crystal structure brainly.com/question/5048216

Keywords: density, our sun will end up as a white dwarf, reduced to about 15,000 km in diameter, mass, volume of the sphere, in about 5 billion years, at the end of its lifetime